Stars and bars (non-negative integers) (Non-negative integer solutions count: C(n+r−1, r−1) or C(n+r−1, n))

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Non-negative integer solutions count: C(n+r−1, r−1) or C(n+r−1, n)

What each symbol means

SymbolWhat it stands for
n,rTotal sum n, number of variables r

When to use this

Non-negative integers; order of variables fixed.